A particle swarm–BFGS algorithm for nonlinear programming problems

This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle swarm optimization to solve augmented Lagrangian penalty function. In doing so, the algorithm launches into a global search over the solution space while keeping a detailed exploration into the neighborhoods. To shed light on the merit of the algorithm, we provide a test bed consisting of 30 test problems to compare our algorithm against two of its variations along with two state-of-the-art nonlinear optimization algorithms. The numerical experiments illustrate that the proposed algorithm makes an effective use of hybrid framework when dealing with nonlinear equality constraints although its convergence cannot be guaranteed.     

Efficient implementation of a generalized polak-ribière algorithm for nonlinear optimization

We have recently developed a new conjugate gradient type method, the Generalized Polak-Ribière (GPR) method, for unconstrained minimization. It is based on search directions that are parallel to the Newton direction of the restriction of the objective function f on the two dimensional subspace span{?g p}, with p a suitable direction in span{? g,s^?}, where g and s ^? are the current gradient and previous search direction respectively. The new approach proved to be considerably more efficient than the original Polak-Ribière method.

In this paper, various implementations of the GPR method are compared with a currently available standard NAG software routine and also with the Nocedal, Buckley-LeNir and Shanno's limited memory algorithms. The results demonstrate the general effectiveness of the new algorithm. We also give a very brief discussion of extensions of the GPR method that generate search directions parallel to Newton directions in subspaces of dimension greater than two.     

Hydrocarbon Index – an algorithm for hyperspectral detection of hydrocarbons

Previous studies have shown that spectral signatures of hydrocarbon-bearing materials are characterized by prominent absorption features at 1.73 and 2.31?µm. Many other materials also show absorption features at wavelengths in the interval from 2.0 to 2.5?µm, yielding a mixed response in spectral signatures. In contrast to this wavelength range, most materials show similar spectral characteristics in the 1.73?µm range. Mainly hydrocarbon-bearing materials produce an absorption feature which is unique and prominent at 1.73?µm. A Hydrocarbon Index (HI) was developed and tested for the direct detection of hydrocarbons. The HI transforms multispectral data into a single image band that shows the distribution of hydrocarbons on the ground surface. The HI takes advantage of reflection differences around the 1.73?µm feature in hydrocarbon spectra. The HI indicates the presence of the 1.73?µm hydrocarbon absorption feature in a pixel spectrum. HI values can be easily calculated from radiance and reflectance data recorded by high signal-to-noise ratio hyperspectral scanners.     

CO2RBFN: an evolutionary cooperative–competitive RBFN design algorithm for classification problems

This paper presents a new evolutionary cooperative–competitive algorithm for the design of Radial Basis Function Networks (RBFNs) for classification problems. The algorithm, CO²RBFN, promotes a cooperative–competitive environment where each individual represents a radial basis function (RBF) and the entire population is responsible for the final solution. The proposal considers, in order to measure the credit assignment of an individual, three factors: contribution to the output of the complete RBFN, local error and overlapping. In addition, to decide the operators’ application probability over an RBF, the algorithm uses a Fuzzy Rule Based System. It must be highlighted that the evolutionary algorithm considers a distance measure which deals, without loss of information, with differences between nominal features which are very usual in classification problems. The precision and complexity of the network obtained by the algorithm are compared with those obtained by different soft computing methods through statistical tests. This study shows that CO²RBFN obtains RBFNs with an appropriate balance between accuracy and simplicity, outperforming the other methods considered.     

An arc-search infeasible interior-point algorithm for horizontal linear complementarity problem in the N∞− neighbourhood of the central path

An arc-search infeasible interior point algorithm is proposed for solving a horizontal linear complementarity problem. The algorithm produces a sequence of iterates in the negative infinity neighbourhood of the central path and searches the solutions along the ellipses that approximate the whole central path. We study the theoretical convergence properties and also establish polynomial complexity bound for the proposed algorithm. Moreover, our numerical results suggest that the proposed algorithm is very efficient and competitive.     

A novel hybrid PSO–GWO algorithm for optimization problems

Engineering with Computers - In this study, we propose a new hybrid algorithm fusing the exploitation ability of the particle swarm optimization (PSO) with the exploration ability of the grey wolf...     

Distributed primal–dual interior-point methods for solving tree-structured coupled convex problems using message-passing

In this paper, we propose a distributed algorithm for solving coupled problems with chordal sparsity or an inherent tree structure which relies on primal–dual interior-point methods. We achieve this by distributing the computations at each iteration, using message-passing. In comparison to existing distributed algorithms for solving such problems, this algorithm requires far fewer iterations to converge to a solution with high accuracy. Furthermore, it is possible to compute an upper-bound for the number of required iterations which, unlike existing methods, only depends on the coupling structure in the problem. We illustrate the performance of our proposed method using a set of numerical examples.     

Parameterized eigensolution technique for solving constrained least squares problems ∗

This paper aims to introduce an algorithm for solving large scale least squares problems subject to quadratic inequality constraints. The algorithm recasts the least squares problem in terms of a parameterized eigenproblem. A variant of k-step Arnoldi method is determined to be well suited for computing the parameterized eigenpair. A two-point interpolating scheme is developed for updating the parameter. A local convergence theory for this algorithm is presented. It is shown that this algorithm is superlinearly convergent.     

An algorithm of contact problems for forming process of thin plates—a numerical analysis for the seaming process of a can

An algorithm of contact problems for processing thin plates is presented. In the seaming process of a can, two thin plates, an end and flange of a can slip each other and repeat contacting and separating, and are deformed by a roll. To analyse such a complex contact problem, an algorithm using penalty forces and maximum displacement control is proposed. A trial analysis of the seaming process with this algorithm is shown in this paper.     

Modification of a two-dimensional fast Fourier transform algorithm with an analog of the Cooley–Tukey algorithm for image processing

Two-dimensional fast Fourier transform (FFT) for image processing and filtering is widely used in modern digital image processing systems. This paper concerns the possibility of using a modification of two-dimensional FFT with an analog of the Cooley–Tukey algorithm, which requires a smaller number of complex addition and multiplication operations than the standard method of calculation by rows and columns.     

Numerical computation of the optimal feedback law¶for nonlinear infinite time horizon control problems

An approach to the numerical computation of the optimal feedback law for nonlinear infinite time horizon control problems is presented and tested. For a sequence of control systems with truncated time horizon the canonical equations are solved by an adapted multiple shooting algorithm. Interpolation of computed costates gives a feedback law on a prescribed region of the state space. Numerical findings indicate applicability of this procedure to problems in higher dimensions. Received: February 1999 / Accepted: July 1999     

A linear Uzawa-type FEM–BEM solver for nonlinear transmission problems

We propose a fully discrete Uzawa-type iteration for the Johnson–Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular integral equation associated with the Laplace-operator and one FEM for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to build the right-hand side of the Yukawa equation. The algorithm includes the inexact solution of the BEM/FEM part by a preconditioned CG method. We prove that the proposed method leads to linear convergence with respect to the number of Uzawa iterations. Moreover, while the current analysis of a direct FEM–BEM discretization of the Johnson–Nédélec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.     

KSpheres – an efficient algorithm for joining skinning surfaces

Besides classical point based surface design, sphere based creation of characters and other surfaces has been introduced by some of the recently developed modeling tools in computer graphics. ZSpheres^® by Pixologic, or Spore™ by Electronic Arts are just two prominent examples of these softwares. In this paper we introduce a new sphere based modeling tool, which allows us to create smooth, tubular-like surfaces by skinning a user-defined set of spheres. The main advantage of the new method is to provide a parametric surface with more natural and smoother shape, especially at the connection of branches than the surfaces provided by the existing softwares and methods.